# NAPLEX Question of the Week: Calculations

Whether it is counting down the days to graduation or counting a 30-days prescription supply of a medication for your patient, calculations play an important role in pharmacy.

AM is a 59 yo male (5’10”; 164 lbs) who presents to the hospital after cardiac arrest where he was found down and unresponsive at home. ACLS was performed in the ambulance. Upon arrival to the hospital, the patient was found to have pulseless ventricular tachycardia not responding to epinephrine or cardioversion. Additional options were discussed leading to the recommendation of lidocaine. A one time IV loading dose of 1.5 mg/kg was already given in the ED. The ED nurse is now hanging a 2% lidocaine drip at 0.5 mg/kg/min. How many hours would a 250 mL bag last? Round the answer to the nearest tenth.

Test taking tip: As mentioned before, especially with calculations, it is important to know what the question is asking for in order to not get confused by all the details in the case or question. You also really want to focus on the specific units within the question. While you are in a testing environment it can be easy to do all your math correctly but not give the appropriate answer based on units. If a calculation question is associated with constructed-response question types, you will just have a blank box to fill in, so it is important to be attentive. Be aware of some cases that provide you with more information than you actually need to solve the question (like the loading dose information in this question). One of the question types shown in the NABP NAPLEX bulletin is a constructed-response question (i.e. fill in the blank), which uses a calculations based question as the example - https://nabp.pharmacy/wp-content/uploads/2019/03/NAPLEX_MPJE_Bulletin_2020.pdf

Rationale:

Using the tip above, you will see we are looking for a length of time in hours for this question. Now you have to see what information is provided for you. You have a concentration of drug (w/v), a weight of the patient, a dosing rate, and a total volume of the bag of medication. In this case you will need to use all components provided. First, you need to find out how much drug is in the total volume of the 250 mL bag in order to help calculate how long the bag will last.

w/v % concentration is correlated to how many g/100 mL there are. In this example 2% correlates to 2g/100mL. You will then need to set up a ratio to determine how many grams are in 250 mL.

2g/100 mL = x g/250mL

x = 5 g

Now you have a rate based on mg/kg/min. You know you have 5g of drug contained in the 250 mL bag. Remember it is always important to focus on units.

Convert the weight provided to you to kg (lbs/2.2 = x kg) so 164 pounds = ~74.5 kg

Now you have all the information you need to calculate how many hours the total volume (250 mL) will run:

0.5 mg/kg/min x 74.5 kg = 37.5 mg/min

[5g x (1000mg/g)]/37.5 mg/min = ~133.3 min

133.3 min x 1hr/60 min = 2.2 hours which is the correct answer.

There are different ways to get to the same answer, but always remember to check your units and ensure they cancel out as you are working your way to the final answer. Also pay attention to the rounding instructions as shown here the instructions said to round your answer to the nearest tenth.

### Christopher M. Bland

Clinical Associate Professor, University of Georgia College of Pharmacy